Question

Prove that: $\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}+5\ge (a+b)(b+c)(c+a)$

score 165 · Answer 1 · 2026-04-16 00:41:24

165

Views

Prove that: $\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}+5\ge (a+b)(b+c)(c+a)$

Published on 16 Apr 2026 - 0:41

score 498 · Answer 2 · 2026-04-16 05:17:09

498

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How to show that $\lim_{n\to \infty} \frac{a_1 +a_2 + \cdots + a_n}{n} = 0?$

Published on 16 Apr 2026 - 5:17

score 51 · Answer 3 · 2026-04-11 19:34:57

51

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Let $f : [a, \infty) \to \mathbb R$ be an integrable function on each $[a, r], r \gt a$...

Published on 11 Apr 2026 - 19:34

score 94 · Answer 4 · 2026-04-15 13:19:01

94

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Alternative proofs to integral test that $\lim_{n\to\infty}\sum_{j=1}^n \alpha^{j^p}$ converges; $0<\alpha,p<1.$

Published on 15 Apr 2026 - 13:19

score 76 · Answer 5 · 2026-04-16 01:37:36

76

Views

Given $7$ blank spaces and four letters $A,B,C,D$, what is the number of ways each space can be filled up so that all four letters are used up.

Published on 16 Apr 2026 - 1:37

score 104 · Answer 6 · 2026-04-14 09:10:53

104

Views

Does this variant of Cantor's diagonal argument work?

Published on 14 Apr 2026 - 9:10

score 74 · Answer 7 · 2026-04-17 09:30:59

74

Views

$K\subseteq X$ is compact iff every net in $K$ has an accumulation point in $K$

Published on 17 Apr 2026 - 9:30

score 59 · Answer 8 · 2026-04-14 11:01:41

59

Views

Is there some other ways to prove "If $V,W$ are both finite-dimensional, then $L(V,W)$ is finite-dimensional.

Published on 14 Apr 2026 - 11:01

score 156 · Answer 9 · 2026-04-10 15:50:52

156

Views

Evaluating the infinite sum $ \sum_{k=1}^\infty \frac{H_k}{k^4}$

Published on 10 Apr 2026 - 15:50

score 43 · Answer 10 · 2026-04-15 19:37:57

43

Views

Evaluating $\lim_{n\to\infty}\sum_{i=1}^n \left(\frac{i}{n}\right)^n$

Published on 15 Apr 2026 - 19:37

score 55 · Answer 11 · 2026-04-16 22:00:41

55

Views

Direct proof for "If for every sequence $(x_n)$ such that $\lim x_n = a$ it's true that $\lim f(x_n) = f(a)$, then $f$ is continuous"

Published on 16 Apr 2026 - 22:00

score 109 · Answer 12 · 2026-04-15 22:46:48

109

Views

Proving $\sum_{n=0}^\infty\left(\frac{x^n}{n!}\right)^2$ is continuous on $\mathbb{R}$. ISI PCB 2020

Published on 15 Apr 2026 - 22:46

score 124 · Answer 13 · 2026-04-16 23:56:19

124

Views

If $\max\limits_{|z|=1/2}|f(z)| = |a_4|/2^4$, then $f(z) = a_4z^4$.

Published on 16 Apr 2026 - 23:56

score 41 · Answer 14 · 2026-04-13 12:12:48

41

Views

Vector solution to an angle bisector problem?

Published on 13 Apr 2026 - 12:12

score 30 · Answer 15 · 2026-04-11 11:28:49

30

Views

Confusion about alternative unit interval connectedness proof

Published on 11 Apr 2026 - 11:28

List Question

Prove that: $\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}+5\ge (a+b)(b+c)(c+a)$

How to show that $\lim_{n\to \infty} \frac{a_1 +a_2 + \cdots + a_n}{n} = 0?$

Let $f : [a, \infty) \to \mathbb R$ be an integrable function on each $[a, r], r \gt a$...

Alternative proofs to integral test that $\lim_{n\to\infty}\sum_{j=1}^n \alpha^{j^p}$ converges; $0<\alpha,p<1.$

Given $7$ blank spaces and four letters $A,B,C,D$, what is the number of ways each space can be filled up so that all four letters are used up.

Does this variant of Cantor's diagonal argument work?

$K\subseteq X$ is compact iff every net in $K$ has an accumulation point in $K$

Is there some other ways to prove "If $V,W$ are both finite-dimensional, then $L(V,W)$ is finite-dimensional.

Evaluating the infinite sum $ \sum_{k=1}^\infty \frac{H_k}{k^4}$

Evaluating $\lim_{n\to\infty}\sum_{i=1}^n \left(\frac{i}{n}\right)^n$

Direct proof for "If for every sequence $(x_n)$ such that $\lim x_n = a$ it's true that $\lim f(x_n) = f(a)$, then $f$ is continuous"

Proving $\sum_{n=0}^\infty\left(\frac{x^n}{n!}\right)^2$ is continuous on $\mathbb{R}$. ISI PCB 2020

If $\max\limits_{|z|=1/2}|f(z)| = |a_4|/2^4$, then $f(z) = a_4z^4$.

Vector solution to an angle bisector problem?

Confusion about alternative unit interval connectedness proof

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